Determination of the Jump of a Function of Generalized Bounded Variation by the Derivatives of a Trigonometric Interpolation Polynomial

A. A. Kelzon

Admiral Makarov State Maritime Academy

Abstract: We obtain formulas expressing the value of the jump of a bounded periodic function of harmonic bounded variation in a neighborhood of the point under consideration via the derivatives of odd order of the Lagrange trigonometric interpolation polynomial with equidistant nodes and via the derivatives of even order of the conjugate polynomial.

UDC: 517.518

Received: 15.04.2002

DOI: 10.4213/mzm90

 English version: Mathematical Notes, 2004, 76:1, 73–80

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